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构造一颗中序遍历是序列的Treap，发现可以很容易地求出序列上第 xx 位的值，即为 getval(root, x) ，但是不好求一个数 kk 在序列上的位置。这时我们就可以维护一个值 idx(k)idx(k) ，表示值为 kk 的节点编号，这时只需要设计出一个函数来求节点 uu 的排名了，而这个函数也很容易实现，对于一个节点 uu ，每次将它向树根跳，如果它是右儿子，那么就将它父亲的左子树的值以及父亲的大小计入结果。

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int getpos(int id) { 
    int f, cnt = 0;
    while ((f = p[id].f) != 0) {
        if (id == p[f].rs) {
            cnt += p[p[f].ls].siz + 1;
        }
        id = f;
    }
    return cnt;
}

既然要存储一个节点的父亲，那么 pushup 更新的时候也要改一下

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void pushup(int u) { 
    int ls = p[u].ls, rs = p[u].rs;
    if (ls) p[ls].f = u;
    if (rs) p[rs].f = u;
    p[u].siz = p[ls].siz + p[rs].siz + 1;
}

下面总结一下遇到的坑。

getpos 函数，cnt = 0 初始化是错的，应该赋值为 cnt = p[p[id].ls].siz + 1 ，先加上位置大于 ff 而小于 idid 的数个数和 idid 本身。调了我一个小时，一个一个函数地检查

full code:

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#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>

const int MAXN = 8e4 + 10;

struct Node {
    int ls, rs, f;
    int val;
    int siz;
    int rnd;
}p[MAXN << 5];

int n, m, tot, root;
int idx[MAXN];

void _fullvis(int u) {
    if (p[u].ls) _fullvis(p[u].ls);
    printf("    node #%d: val=%d, son=#%d/#%d, f=#%d, siz=%d, rnd=%d\n", u, p[u].val, p[u].ls, p[u].rs, p[u].f, p[u].siz, p[u].rnd);
    if (p[u].rs) _fullvis(p[u].rs);
}

void _fulldisplaytree(int u, std::string s) {
    printf("full display of tree '%s[%d]' {\n", s.c_str(), u);
    _fullvis(u);
    puts("}\n");
}

void _middlevis(int u) {
    if (p[u].ls) _middlevis(p[u].ls);
    printf("%d ", p[u].val);
    if (p[u].rs) _middlevis(p[u].rs);
}

void _displaytree(int u, std::string s) {
    printf("display of tree '%s[%d]' { ", s.c_str(), u);
    _middlevis(u);
    printf("}\n");
}

int newnode(int val) {
    tot++;
    p[tot].val = val;
    p[tot].ls = p[tot].rs = 0;
    p[tot].siz = 1;
    p[tot].rnd = rand();
    return tot;
}

void pushup(int u) { 
    int ls = p[u].ls, rs = p[u].rs;
    if (ls) p[ls].f = u;
    if (rs) p[rs].f = u;
    p[u].siz = p[ls].siz + p[rs].siz + 1;
}

void sizsplit(int rt, int &a, int &b, int rank) {
    if (rt == 0) {
        a = b = 0;
        return;
    }
    int siz = p[p[rt].ls].siz;
    if (siz + 1 <= rank) {
        a = rt;
        sizsplit(p[rt].rs, p[a].rs, b, rank - siz - 1);
        pushup(a);
    } else {
        b = rt;
        sizsplit(p[rt].ls, a, p[b].ls, rank);
        pushup(b);
    }
}

//void valsplit(int rt, int &a, int &b, int val) {
    //if (rt == 0) {
        //a = b = 0;
        //return;
    //}
    //if (p[rt].val <= val) {
        //a = rt;
        //valsplit(p[rt].rs, p[a].rs, b, val);
        //pushup(a);
    //} else {
        //b = rt;
        //valsplit(p[rt].ls, a, p[b].ls, val);
        //pushup(b);
    //}
//}

void merge(int a, int b, int &rt) {
    if (a == 0 || b == 0) {
        rt = a + b;
        return;
    }
    if (p[a].rnd <= p[b].rnd) {
        rt = a;
        merge(p[a].rs, b, p[rt].rs);
        pushup(rt);
    } else {
        rt = b;
        merge(a, p[b].ls, p[rt].ls);
        pushup(rt);
    }
}

void insert(int pos, int val) {
    int x, y, z;
    sizsplit(root, x, y, pos - 1);
    int u = newnode(val); idx[val] = u;
    merge(x, u, z);
    merge(z, y, root);
}

int getval(int rt, int pos) {
    int siz = p[p[rt].ls].siz;
    //printf("getval of (%d, %d)\n", rt, pos);
    //_displaytree(rt, "rt");
    //printf("siz=%d\n", siz);
    if (siz + 1 < pos) {
        return getval(p[rt].rs, pos - siz - 1);
    } else if (siz + 1 > pos){
        return getval(p[rt].ls, pos);
    } else {
        return p[rt].val;
    }
}

int getpos(int id) { 
    int f, cnt = p[p[id].ls].siz + 1;
    while ((f = p[id].f) != 0) {
        if (id == p[f].rs) {
            cnt += p[p[f].ls].siz + 1;
            //printf("add cnt %d\n", p[p[f].ls].siz + 1);
        }
        id = f;
    }
    return cnt;
}

void putup(int val) {
    int pos = getpos(idx[val]);
    int x, y, a, b;
    sizsplit(root, x, y, pos - 1);
    //_displaytree(x, "x"); _displaytree(y, "y");
    sizsplit(y, a, b, 1);
    merge(a, x, y);
    merge(y, b, root);
}

void putdown(int val) {
    //printf("idx[%d]=%d\n", val, idx[val]);
    int pos = getpos(idx[val]);
    int x, y, a, b;
    //printf("pos[%d]=%d\n", val, pos);
    sizsplit(root, x, y, pos - 1);
    //_displaytree(x, "x"), _displaytree(y, "y");
    sizsplit(y, a, b, 1);
    merge(b, a, y);
    merge(x, y, root);
}

void move(int val, int to) {
    if (to == 0) return;
    int pos = getpos(idx[val]), u = idx[val];
    int nextval = getval(root, pos + to);
    int v = idx[nextval];
    p[u].val = nextval;
    p[v].val = val;
    idx[val] = v;
    idx[nextval] = u;
}

int ask(int s) {
    //printf("ask(%d): %d-%d\n", s, idx[s], getpos(idx[s]));
    return getpos(idx[s]) - 1;
}

int query(int s) {
    return getval(root, s);
}

int main() {
    scanf("%d%d", &n, &m);
    for (int i = 1, p; i <= n; i++) {
        scanf("%d", &p);
        insert(i, p);
    }
    char opt[10];
    for (int i = 1, s, t; i <= m; i++ ) {
        scanf("%s", opt);
        //printf("operator #%d(%s)\n", i, opt);
        switch (opt[0]) {
            case 'T':
                scanf("%d", &s);
                putup(s);
                break;
            case 'B':
                scanf("%d", &s);
                putdown(s);
                break;
            case 'I':
                scanf("%d%d", &s, &t);
                move(s, t);
                break;
            case 'A':
                scanf("%d", &s);
                printf("%d\n", ask(s));
                break;
            case 'Q':
                scanf("%d", &s);
                printf("%d\n", query(s));
                break;
        }
        //_fulldisplaytree(root, "root");
    }
    return 0;
}